Study On The Safety Analysis For A Class Of Continuous Nonlinear Dynamic Systems

The operational processes of large-scale dynamic systems,such as chemical process systems,power systems,and high-speed railway systems,often involve high energy accumulation,high temperature,high pressure,and high speed.Therefore,it is very strict that the safety requirements of these dynamic systems are.For these energy-intensive operational processes,if dangerous factors,including abnormal operational states and system faults,etc.,cannot detected or dealt with in time,a large amount of energy may be released fast in a short time,such that it may lead to accidents.Thus,how to ensure a system can be safe,especially how to maintain the safe state of the system after the dangerous factors like faults being stimulated,has been the main research category of the dynamic system safety.Among them,the study which is how to analyze,identify and predict the changes of the safety states for a dynamic system,has been playing an important role in the construction of an integrated active safety control framework of "fault online estimation?safety judgment and identification?state control under safety constraints".Oriented to fault estimation and state control involved in system safety,this paper takes system dynamic models as the entry point for safety research,closely focuses on the core which is the analysis and evolution prediction of the dynamic system safe states,digs deep into the system safety analysis theories for a class of classic continuous nonlinear dynamic systems and two special systems in this class of systems—periodical characteristic system and strict safety system,and puts forward a variety of system safety criteria based on several different kinds of barrier functions.And then,it establishes Multi-Hyperspheres barrier function construction method and the barrier function construction method based on archipelago-bridge segmentation.The main content of the paper can be summarized as the following aspects:(1)It proposes the safety criteria based on exponential barrier functions.It formulates a novel kind of relaxed safety criteria for dynamic system based on exponential barrier functions for a general class of continuous nonlinear dynamic systems,by relaxing the bounded range of the first derivative function of the barrier function.And on this basis,it puts forward the related fault-safety criteria when a smooth and observable fault of the dynamic system occurs.These criteria expand the scope of application of the safety criteria,and provide a basis for the fusion of safety constraint control,finite time stability control,and Lyapunov exponential stability control.(2)It proposes a series criteria of safety based on extreme-value barrier functions.Aiming at the problem that it is difficult to maintain monotonicity of the time-varying relative distance between the running state trajectory and the unsafe state set for a kind of period-like dynamic systems,a weak behavior constraint condition considering the distribution of extreme points of the barrier function is proposed to form the safety criteria of the systems based on the extreme-value barrier functions.And for some kind of smooth and observable fault occured at a certain moment of system operational process,this paper proposes the corresponding fault-safety criteria.By simulation,the validity of the proposed safety criteria and safety control laws are verified.These criteria can allow the monotonicity of the barrier functions to fluctuate or change within an acceptable range,which effectively supplement the existing safety analysis theories of dynamic system based on the barrier functions.(3)It proposes a set of safety criteria based on Class X barrier functions.In view of the difficulty of obtaining a complete set of unsafe states for strictly safe dynamic systems,it puts forward a class of Class M barrier functions and Class D barrier functions and the corresponding safety criteria for strict safety systems,which are proposed only based on the safety state set with safety strictness.With the use of the forward invariance theory,the rationality and correctness of the safety criteria can be proved.In addition,for a class of typical nonlinear dynamic control systems,it establishes the control barrier functions and the corresponding control laws.By simulation examples,the correctness of the theory is theoretically verified.It provides a certain theoretical basis for realizing the system control under the safety constraints that meet the actual dynamic system characteristics.(4)The barrier function construction method based on the Multi-hypersphere method is established and improved.Aiming at the fact that the safe state sets or unsafe state sets of the actual process systems have the characteristics of complex configuration,multiple state subsets,complex connectivity and non-convex,etc.,it proposes a positive multi-hypersphere barrier function construction method.And for three special spatial relations between the safe state set and unsafe state set,it proposes a reverse multi-hypersphere barrier function construction method.The Multi-hypersphere method is helpful to design the system state controllers under safety constraints using the safety criteria based on the barrier functions.(5)It establishes a barrier function construction method based on archipelago-bridge segmentation.Considering that the feasible state set of the dynamic system has the characteristics of multiple operating conditions or multiple independent subsets and the characteristics of complex connectivity and irregular geometric shapes,the barrier functions under the archipelago safe set and under the archipelago-bridge safe set are constructed respectively.Based on these,it proposes a series of the relevant system safety definitions,safety criteria,and corresponding system state control laws under safety constraints.On the basis of the above theoretical analysis and simulation verification,in the end,it lists the summary and analysis of the main work and research results of the paper,the limitations of existing research,and the next sustainable research directions which we can do.